Elliptic curve search results

Results (5 matches)

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Label	Class	Class size	Class degree	Base field	Field degree	Field signature	Conductor	Conductor norm	Discriminant norm	Root analytic conductor	Bad primes	Rank	Torsion	CM	CM	Sato-Tate	$\Q$-curve	Base change	Semistable	Potentially good	Nonmax $\ell$	mod-$\ell$ images	$Ш_{\textrm{an}}$	Tamagawa	Regulator	Period	Leading coeff	j-invariant	Weierstrass coefficients	Weierstrass equation
98.1-a2	98.1-a	$12$	$36$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	98.1	\( 2 \cdot 7^{2} \)	\( 2^{4} \cdot 7^{2} \)	$0.79523$	$(a), (-2a+1), (2a+1)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.1	$1$	\( 2 \)	$1$	$35.33144352$	0.693975091	\( -\frac{15625}{28} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-{x}$
686.1-d2	686.1-d	$12$	$36$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	686.1	\( 2 \cdot 7^{3} \)	\( 2^{4} \cdot 7^{8} \)	$1.29349$	$(a), (-2a+1), (2a+1)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	\( 2^{4} \)	$1$	$5.955778371$	2.105685636	\( -\frac{15625}{28} \)	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -3 a - 6\) , \( -6 a - 7\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a-6\right){x}-6a-7$
686.2-d2	686.2-d	$12$	$36$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	686.2	\( 2 \cdot 7^{3} \)	\( 2^{4} \cdot 7^{8} \)	$1.29349$	$(a), (-2a+1), (2a+1)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	\( 2^{4} \)	$1$	$5.955778371$	2.105685636	\( -\frac{15625}{28} \)	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( a - 6\) , \( 5 a - 7\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(a-6\right){x}+5a-7$
784.1-a2	784.1-a	$12$	$36$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	784.1	\( 2^{4} \cdot 7^{2} \)	\( 2^{16} \cdot 7^{2} \)	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B	$1$	\( 2^{2} \)	$1$	$3.513854052$	1.242335014	\( -\frac{15625}{28} \)	\( \bigl[a\) , \( -1\) , \( 0\) , \( -2\) , \( -2\bigr] \)	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-2{x}-2$
4802.1-z2	4802.1-z	$12$	$36$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	4802.1	\( 2 \cdot 7^{4} \)	\( 2^{4} \cdot 7^{14} \)	$2.10397$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B	$1$	\( 2^{3} \)	$1$	$1.003958300$	0.709905722	\( -\frac{15625}{28} \)	\( \bigl[1\) , \( 1\) , \( 0\) , \( -25\) , \( -111\bigr] \)	${y}^2+{x}{y}={x}^{3}+{x}^{2}-25{x}-111$

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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.